Vinod Kathail. Optimal interpreters for lambda-calculus based functional languages. Ph.D. Thesis, MIT, May 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....position to identify similar redexes whose reduction should somehow be evaluated at once (via a so called parallel reduction) by any ecient scheme. Recent research by Lamping, and independently Kathail, has shown that there indeed exist calculus evaluators satisfying L evy s speci cation [Lam90, Kat90]. Lamping introduced a beautiful graph reduction technology for sharing evaluation contexts dual to the sharing of values. His pioneering insights have been modi ed and improved in subsequent implementations of optimal reduction, most notably by Asperti, and by Gonthier, Abadi, and L evy [Asp94, ....

Vinod Kathail. Optimal interpreters for lambda-calculus based functional languages. Ph.D. Thesis, MIT, May 1990.

....it was e ective, but no one knew at that time what kind of data structure could be used to dynamically maintain the families in such a way that all the redexes of a given family could be somehow shared and, therefore, reduced as a single step. The solution came in 1989, when independently Kathail [Kat90] and Lamping [Lam90] gave abstract calculus machines which reduced terms as prescribed by L evy s optimality theory. Lamping s graph rewriting approach is the one that received most interest, and after his breakthrough other variants of optimal reducers have been proposed, especially by ....

Vinod K. Kathail. Optimal Interpreters for Lambda-calculus Based Functional Programming Languages. PhD thesis, MIT, May 1990.

....where a similar expression [ x : M ] is defined. It spawns a new computation of M for every occurence of x. this reason the ffi calculus is appropriate to describe implementations of lazy and eager calculus. We should remark that the ffi calculus is unable to model optimal reduction [GAL, Lam90, Kat90], since it prohibits reduction in abstractions. The ffi calculus is one of several calculi [Smo93] describing aspects of the multi paradigm programming language Oz [Smo94] All those calculi use relational settings as does the ffi calculus. Oz has been developed in parallel with those calculi ....

Vinod Kathail. Optimal interpreters for lambda--calculus based functional languages, 1990. PHD-Thesis, MIT.

....of just these nodes as in this paper we postponed this move for the sake of the brevity of presentation. One important direction for further research would be to extend the approach to be able to tackle the term graph representation systems used for optimal reduction in the # calculus such as [40, 42, 30, 25, 16, 2]. In the second aspect of this paper we stress the usefulness of relational notation and calculus we strongly feel that the results in [21, 22] and in this paper would not have been achieved without. Although some concepts require a second thought for understanding, the relational ....

Vinod Kathail. Optimal Interpreters for Lambda-Calculus Based Functional Languages. PhD thesis, MIT, May 1990.

....is not the absolute position of a layer in an environment but its position relative to other layers. In particular, joining two environments A and B with renaming is immediately achieved by concatenating the two environments into 5 This approach of structure sharing is partially inspired by[Kat90, CHL92] where substitutions are represented by operators which forms a calculus. JOIN A B A x B B t k AxB t (k A ) A t k AxB t k Figure 3: Environment join an environment A Omega B, as shown in Fig. 3. Terms of A remain unchanged in A Omega B, while terms of B are shifted by the ....

Vinod Kumar Kathail. Optimal Interpreters for Lambda--calculus Based Functional Languages. PhD thesis, M.I.T., 1990.

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